Fibonacci Sequence and Golden Ratio in Plastic Surgery

Many artists have established the ratios of the human body. Among them, Leonardo Da Vinci presented his very famous Vitruvian man whose umbilicus is the center of a circle passing at the limit of his four outstretched limbs. In the 20th century, the French architect Le Corbusier gave us the relative dimensions of the whole human body.

Originally, Le Corbusier expressed rather skeptical, and even negative, views of the application of the Golden ratio to art, warning against the “replacement of the mysticism of the sensibility by the Golden Section.” In fact, a thorough analysis of Le Corbusier’s architectural designs and “Purists” paintings by Roger Herz-Fischler shows that prior to 1927, Le Corbusier never used the Golden ratio. This situation changed dramatically following the publication of Matila Ghyka’s influential book Aesthetics of Proportions in Nature and in the Arts.

Le Corbusier’s fascination with Aesthetics and with the Golden Ratio had two origins. On one hand, it was a consequence of his interest in basic forms and structures underlying natural phenomenon. On the other, coming from a family that encouraged musical education, Le Corbusier could appreciate that Pythagorean craving for a harmony achieved by number ratios. He wrote: “More than these thirty years past, the sap of mathematics has flown through the veins of my work, both as an architect and painter; for music is always present within me.” Le Corbusier’s search for a standardized proportion culminated in the introduction of a new proportional system called the “Modulor.”

The Modulor was supposed to provide “a harmonic measure to the human scale, universally applicable to architecture and mechanics.” In the spirit of Vitruvian man and the general philosophical commitment to discover a proportion system equivalent to that of natural creation, the Modulor was based on human proportions.

A six-foot (about 183-centimeter) man, with his arm upraised (to a height of 226 cm; 7’5”), was inserted into a square . The ratio of the height of the man (183 cm; 6’) to the height of his navel (at the mid-point of 113 cm; 3’8.5”) was taken precisely in a Golden Ratio.

The total height (from the feet to the raised arm) was also divided in a Golden ratio (into 140cm and 86 cm) at the level of the wrist of a downward-hanging arm. The two ratios (113/70) and (140/86) were further subdivided into smaller dimensions according to the Fibonacci series.

Le Corbusier developed the Modulor between 1943 and 1955 in an era which was already displaying widespread fascination with mathematics as a potential source of universal truths.

The Modulor is the proportioning system developed by Le Corbusier based on the Fibonacci series (1,1,2,3,5,8,13). He believed these proportions to be evident in the human body. The Fibonacci series is also the closest approximation in whole numbers to the Golden Section. The purpose of the Modulor was to "maintain the human scale everywhere".

In addition to existing in nature, art and architecture, it has been hypothesized that great classical composers like Mozart had an awareness of the Golden Ratio and used it to compose some of his famous sonatas.

Mozart's piano sonatas have been observed to display use of the golden ratio through the arrangement of sections of measures that make up the whole of the piece. In Mozart's time, piano sonatas were made up of two sections, the exposition and the recapitulation. In a one hundred measure composition it has been noted that Mozart divided the sections between the thirty-eighth and sixty-second measures. This is the closest approximation that can be made to the Golden Ratio within the confines of a one-hundred measure composition.

The Golden Ratio has also appeared in poetry in much the same way that it appears in music. The emphasis has been placed on time intervals. Some have even stated that the meaning of chosen words is less important than its rhythmic quality and the intervals between words and lines that serve to create the overall rhythm of a poem.

Probably the most compelling display of the Golden Ratio is in the many examples seen in nature. The Golden Ratio and the Fibonacci Sequence can be seen in objects from the human body to the growth pattern of a chambered nautilus. Examples of the Fibonacci Sequence can be seen in the growth pattern of a tree branch or the packing pattern of seeds on a flower. Ultimately, this aspect is what has earned the Golden Mean its representation as the Divine Proportion.

It is the prevalence of the Golden Ratio in nature that has influenced classic art and architecture. The great masters developed their skills by recreating things they observed in nature. In the earliest of cases, these artists and craftsmen probably had no knowledge of the math involved, only an acute awareness of this pattern repeated around them. It was the mathematicians that unlocked the secrets of the Golden Ratio. Their work has led to the understanding of the complex mathematical underpinnings hidden within the Golden Mean.

One of the areas of the body subject of study in our specialty, in terms of proportions is the face. Leslie Farkas, in the plastic surgery field, may be described as the pioneer of modern craniofacial anthropometry. His lifelong devotion to research in craniofacial anthropometry generated a detailed body of work over nearly half a century that represents a major contribution to our understanding of the craniofacial complex. He made a major contribution to our understanding of how anthropometry relates to the face and head in normalcy, beauty, and deformity during the last 25 years. His books and numerous articles have generated a detailed body of work of anthropometric data. His work examined the anthropometric relationships and measurements of children and adults, normal and attractive individuals, and subjects of different ethnic groups.

Farkas studied the neoclassical canons and found them to be variably represented in actual human subjects. Studies in the early 1990s by Judith Langlois and Lori A. Roggman concluded that empirical evidence supported the notion that the most attractive faces in a given population favored characteristics close to the mean of the population. It was reasoned that selection favored normative features adaptive for survival within the local environment. This theory, which is based on natural selection, offers a plausible explanation for why average faces may be considered attractive, how these preferences could have been acquired, and why cultural differences would occur. However, subsequent experiments have challenged this theory, and new data suggest that the most "attractive" faces vastly differ from the average in a systematic and reproducible manner.

In plastic and reconstructive surgery, we always look to achieve the ideal proportions, which are applicable to make various aesthetic and reconstructive procedures, and this is based on getting natural results because upon any view there will be no single focal point, if not a balance of parties.

One of the features in the face and body analysis to take into account is the symmetry, as always occurs disparity of both sides of the body, so the procedure will improve the contour often different on one side than the other. I think that symmetry has to be seen in vertical, horizontal and depth components, so the analysis is made in a tridimensional way under a critical eye, and analyzing structure by structure, which guide us to do what is necessary to create a balance. One of the clearest examples is the patient who wants to improve their nose, who often worry that the nose is not right for the face after a rhinoplasty, and question if their face will change?

If we don´t take into account the structures of the face, such as the cheeks, eyelids, eyebrows, lips, chin, and mouth, and even more, the transition areas and angles of the nose with all the surrounding structures, probably the whole face will change, and somehow the process will focus only on the nose.

The plastic surgeon, always looks for the balance between all components, to bring the harmony of all parts, and you would be amazed of the results after a procedure such as rhinoplasty, breast augmentation, facial rejuvenation etc., revealing the beauty of the parts that did not undergo for cosmetic improvement during the procedure, and the treated area will not be the focal or distraction point when you look in front of a mirror.